American cheese is “pasteurized, process cheese”. It really, truly, is real cheese. It’s not the most distinctive cheese and often mocked, but it is real cheese.
However -
Most people who think they have eaten or are eating “American cheese” are not, in fact, eating cheese. These days it goes by name "cheese product " but you might also see “cheese food” or something of the sort. Those might have a bit of cheese in them but they also have a crapload of extenders and fillers and other things which are cheaper than actual cheese, even an unrespected cheese such as American cheese.
Kraft singles are “cheese product”, not cheese
Kraft Deli Deluxe are actual American cheese.
Read the labels. It’s important.
Another brand of cheese that is also a “pasteurized process cheese” that does not seem to have the same lack of respect (in America - in its native France I gather it’s not considered a serious cheese) is Laughing Cow (in French, La Vache Qui Rit. I guess people think that because it’s from France it’s a cut above other processed cheeses. Read the label. I know any number of people are are convinced that somehow it’s more of a cheese than American cheese but it’s not. And there’s nothing wrong with either of them really. American cheese is closer to cheddar in flavor (traditionally, a mix of Colby and cheddar), and the original Laughing Cow was Swiss cheese, but they’re both processed cheeses.
Processed cheeses are mass produced with an emphasis on consistency, they are not artisanal cheese made in small batches. Gourmet/artisanal cheeses are meant to have a strong character and they vary. Processed cheeses are meant to always be the same. Two different niches.
One clue is that if each slice must be wrapped or they will all melt into each other then it’s not cheese, it’s “cheese product” or whatever. If slices will remain slices when stacked on top of each other then it’s most likely actual cheese.
Now, IF you intend to melt your cheese or “cheese” then the “cheese product” might be your preferred choice. Velveeta, for example, is a “cheese product” that is promoted as a choice for melting onto cheeseburgers, making grilled cheese sandwiches, various sauces, and dips, and for mac-n-cheese and it is a good choice for that because it melts at a lower temperature and the result has a more consistent texture than a true cheese.
It’s also a “good” choice for school cafeterias and fast food cheeseburgers because it’s cheaper.
Processed cheese also melts well, but not quite as well as “cheese product” or its variations. And processed cheese melts better than non-processed cheeses like cheddar or other hard cheeses.
Want a cheese board with your wine tasting? Get some artisanal cheese for that. Want something for an informal party appetizer or snack? Get some American cheese or Laughing Cow or something similar. Want a cheese burger? Go for “cheese product” unless you want a particular flavor of some other cheese variant. Having Jewish friends over? Don’t serve cheese on the burgers (unless they specifically ask for one - not all Jews keep kosher and my Jewish dad’s liking for ham and Swiss on rye was well known, which is about as un-kosher as a sandwich gets).
In the US “processed cheese” has to be 51% cheese and a few other requirements. Less than that it’s “cheese flavored” something-something. Cheese food is what you feed your pet cheese. (Yes, in the past “cheese food” was a designation used by the industry but not any more due to regulations).